# CALIBUDGET: Calibration-Guided Source Allocation for Fixed-Budget Mixed-Reasoning Adaptation

arXiv: https://arxiv.org/abs/2609.36721 · HTML: https://mlsanity.com/paper/2609.36721/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 45 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 30 of 41)

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- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
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- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
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- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
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- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Super-NaturalInstructions: Generalization via Declarative Instructions on 1600+ NLP Tasks](https://mlsanity.com/paper/2204.07705/) (2022)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)

## Abstract (arXiv)

Fixed-budget adaptation from heterogeneous data sources requires deciding not only how much data to use, but how much exposure each source receives. Size-proportional rules can crowd out small sources, whereas difficulty-only rules can chase noisy estimates or allocate residual budget to nearly saturated pools. We introduce CALIBUDGET, a floor-protected, reliability-aware integer allocator that treats source exposure as an explicit adaptation variable. From small train-internal calibration splits, it combines model need, post-floor availability, and bootstrap stability, then produces exact capacity-respecting quotas without changing the model, objective, or total budget. In a controlled setting combining mathematical and commonsense data, CALIBUDGET improves CommonAvg, FragileAvg, and MacroAvg over validation-error-with-floor, the strongest matched comparator, in all three paired LLaMA-2-7B LoRA+ runs. The respective mean gains are 0.56, 0.46, and 0.41 percentage points (pp). Overall increases by 0.18 pp, whereas MathAvg decreases by 0.20 pp, exposing a coverage-retention boundary rather than a uniform gain. CALIBUDGET changes only 1.14-1.42% of the source budget but improves performance in 15 of 24 comparisons across commonsense tasks and seeds. These results suggest that small changes in source quotas can matter; example-level selection can then determine which examples fill each quota.